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Sine equations

The equation $\sin x = a$ has two solutions during one revolution, as long as $a$ lies between $-1$ and $1$. One is the inverse sine of $a$, and the other is $\pi$ minus the first. Then you can add whole revolutions, $n\cdot 2\pi$. For $a = 1/2$ the first solution is $\pi/6$. You should check both by inserting them into sine.

Symbols

Example

$\sin x = \dfrac{1}{2}$ gives $x = \dfrac{\pi}{6}$, where sine is $0.5$, and $x = \pi - \dfrac{\pi}{6} \approx 2.618$.

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Part of Mathematics R2: Trigonometric functions.